Note: type "help command" to get help on matlab commands, i.e., "help butter."

New:

You may also wish to experiment with the new
Matlab "Filter design and analysis tool." To run this,
type "fdatool" at the Matlab prompt. Use Analysis->FullView to rescale
Y-axis.

matlab < M A T L A B (R) > (c) Copyright 1984-94 The MathWorks, Inc. All Rights Reserved Version 4.2c Dec 31 1994 Commands to get started: intro, demo, help help Commands for more information: help, whatsnew, info, subscribeYou may also want to try:<

>> fsam=4000

>> [z,p,k]=butter(2,6283,'s') z = (NOTE: no finite zeroes in butterworth) [] p = (NOTE:this is location of the 2 poles in s-plane) 1.0e+03 * -4.4428 + 4.4428i -4.4428 - 4.4428i k = 39476089 (NOTE: this is a constant multiplying the result) (==========================) (<<< BEWARE MATLAB BUG!!!) (==========================) Warning: There is an error in the 5.1.0.421 version of matlab. There should be no zeroes in the returned value of z. To fix this, you must suppress the zeroes by entering the command "z=[]" after In the current version you will get z=[ 0 0 0.2500 ] which is wrong! For the new (broken) version, type the following to correct the problem: >> z=[] z = [] >> [n,d]=zp2tf(z,p,k) n = (NOTE: numerator is this constant ) 0 0 39476089 d = 1.0e+07 * (==========================) 0.0000 0.0009 3.9476 (<<< BEWARE MATLAB BUG!!!) (==========================) Warning: There is a bug in some versions of matlab. Although it looks like the values are zero, they are not. The print format is suppressing the significant digits. To fix this use: >> h=tf(n,d,1/fsam) Transfer function: 3.948e07 ----------------------- s^2 + 8886 s + 3.948e07 >> pzmap(h) >> format short e (Now you can see the denominator.) >> d d = (NOTE: denominator is s^2 + 8886 s + 3.9476e+07) 1.0000e+00 8.8855e+03 3.9476e+07 For high order filters, you need even greater numerical precision to avoid errors. So, in this case use: >> format long e >> d d = 1.000000000000000e+00 8.885503812390156e+03 3.947608900000000e+07 >> bode(n,d) You should get this plot >> print analogbut2.eps >> [nd,dd]=impinvar(n,d,4000) nd = (NOTE: numerator = 0 + 2622 z^-1 ) (NOTE: matlab does NOT premultiply by Ts) 1.0e+03 * 0 2.6220 dd = (NOTE: denominator = 1 -0.29 z^-1 + 0.10 z^-2) 1.0000 -0.2925 0.1085 Warning: In the 5.1.0.421 version of matlab, they now seem to be premultiplying by Ts, and so the result now is: >> [nd,dd]=impinvar(n,d,4000) nd = 0 6.5549e-01 0 dd = 1.0000e+00 -2.9248e-01 1.0846e-01 >> freqz(nd,dd,256) You should get this plot Warning: In the current (5.1.0.421) version of matlab, they now seem to be premultiplying by Ts, and so You should get this plot >> print impinvar.eps >>[top,bot]=residuez(nd,dd) (NOTE: use this to find partial fraction form) top = 0- 4.4428e+03i 0+ 4.4428e+03i bot = 1.4624e-01+ 2.9508e-01i 1.4624e-01- 2.9508e-01i (NOTE: Then partial frac expansion is: -4442 i + 4442 i --------------------- --------------------- 1- (.146 + .29 i)z^-1 1- (.146 - .29 i)z^-1 Warning: In the 5.1.0.421 version of matlab, (will they ever get their act together) they now seem to be premultiplying by Ts, and so the result now is: >> [top,bot]=residuez(nd,dd) top = 0 + 1.1107e+00i 0 - 1.1107e+00i bot = 1.4624e-01 - 2.9508e-01i 1.4624e-01 + 2.9508e-01i >> [nd,dd]=bilinear(n,d,4000) nd = 0.2261 0.4523 0.2261 dd = 1.0000 -0.2810 0.1856 >> freqz(nd,dd,256) You should get this plot

>> h=tf(nd,dd,1/fsam)

h =

0.2262 z^2 + 0.4523 z + 0.2262

------------------------------

z^2 - 0.2809 z + 0.1856

>> [nd,dd]=bilinear(n,d,4000,1000) nd = 0.2929 0.5858 0.2929 dd = 1.0000 -0.0000 0.1716 >> freqz(nd,dd,256) You should get this plot >> h=tf(nd,dd,1/fsam) h =

0.2929 z^2 + 0.5858 z + 0.2929

------------------------------

z^2 - 2.22e-16 z + 0.1716 >> pzmap(h) >> zgrid >> zgrid([],[]) >> quit 127007 flops. %